CHAPTER 1, AND PART I: LOCATION

One important contribution The Stag Hunt makes to the social contract literatureFootnote ³ is its refocusing of the discussion upon the Stag Hunt, rather than the Prisoner's Dilemma. The Stag Hunt takes its name from Rousseau's story in A Discourse on Inequality (I shan't describe the game here) and provides a better reformulation of the problem of the social contract for one crucial reason: although the Prisoner's Dilemma illustrates the conflict between individual optimality and collective optimality, All Cooperate is not an equilibrium. Since social contracts are – at least apparently – stable, it seems odd to begin with a game theoretic model that makes a stable social contract rationally impossible. The Stag Hunt better models the problem of the social contract because the “all cooperate” outcome (All Hunt Stag) is an equilibrium as well as the “all defect” outcome (All Hunt Hare). It does not assume the social contract to be rationally impossible at the outset.

This is why Skyrms claims that the problem of social contract formation becomes a problem about equilibrium selection or, alternatively, equilibrium transition. If a society is in a nonequilibrium state (or, heaven forbid, the All Hunt Hare equilibrium, the Stag Hunt representation of the state of nature), how can that society settle upon a social contract – i.e. how can it move into the All Hunt Stag equilibrium? Here we find another argument against using the replicator dynamics to model social evolution: according to those dynamics, the social contract cannot form through gradual means. If society happens to be in the state of nature (All Hunt Hare), under the replicator dynamics any minor deviation (say, any mildly revisionary proposal to move society more closely towards a social contract) will ultimately be discarded, and society will return to the state of nature. It doesn't make sense, argues Skyrms, to model social evolution using dynamics which rule out, a priori, the gradual formation of the social contract. As such, he suggests, we ought to consider alternative dynamics.

The first alternative dynamic considered, and the focus of Part I, are local interaction models. Suppose people are positioned on the squares of a checkerboard and play a game by interacting with their eight nearest neighbors. People receive a total payoff equaling the sum of the payoffs from each pairwise interaction. After everyone has interacted, players engage in a round of strategic learning and modify their strategies. According to the learning rule known as Imitate-the-best, players compare how well they did to their nearest neighbors, and adopt the strategy which received the highest payoff, provided that the highest payoff exceeds the player's current payoff.Footnote ⁴ In contrast, the learning rule known as Best Response assumes that one's neighbors will continue to follow the same strategies in the next generation that they follow in the current generation, and selects the strategy which provides the highest expected payoff. Should a tie between several strategies occur, it is broken with a coin flip.

Given this brief sketch, and without discussing the core results, it should be clear how The Stag Hunt leaves a great deal of interesting ground unexplored. For example, the local interaction models considered in chapters 2 and 3 involve only square lattices and rings (at the very end of chapter 3, Skyrms briefly considers one alternate structure). One may wonder, do the convergence results depend upon the topology of the local interaction model, or the size of the population?Footnote ⁵ What happens if more sophisticated learning rules are employed? What happens if more than one type of learning rule is present in the population? And so the questions multiply. Yet, to my mind, this is a good thing: in its discussion of local interaction models, The Stag Hunt has identified a fertile area of research, and much work remains to be done.

PART II: SIGNALS

Although a natural unity links Part I and Part III, the middle section of The Stag Hunt concentrates on the evolution of inference (chapter 4) and cheap talk (chapter 5), and hence functions more as a conceptual detour than a bridge. The discussion of the evolution of inference revisits Lewis’ well-known signaling game from Convention, and will be familiar to readers of Evolution of the Social Contract from the treatment of the evolution of meaning. The chapter on cheap talk illustrates how, somewhat counter-intuitively, meaningless babble can radically transform the basins of attraction of equilibria in games like the Stag Hunt, in addition to creating entirely new equilibria.

While it is undoubtedly important to show how our inferential capacity could have been produced by evolution as a solution to adaptive problems, the chapter on the evolution of inference is the least developed part of the book and does not actually provide a model of how this might happen. Here we find a conceptual sketch of how one might go about constructing such a model. It would be interesting to see this done, primarily to determine whether the envisioned path from proto-truth functions to full-fledged inference is as easily traveled as intimated.

By contrast, the treatment of Stag Hunt and bargaining games with cheap talk is much more thoroughly fleshed out. Cheap talk – the exchange of costless, meaningless signals over the course of play – has been thought to be relatively ineffective in influencing equilibrium outcomes, even by game theorists such as Robert Aumann. To the extent that cheap talk has been considered effective, it has been thought to primarily destabilize equilibria. Skyrms gives the example of a “secret handshake” used to identify cooperators in the Prisoner's Dilemma. If talk is cheap, mutants which extend the secret handshake yet defect can invade the population.

However, Skyrms shows that both of these views underestimate the power of cheap talk. Cheap talk can create new equilibria, and also can change the size of the basins of attraction in the Stag Hunt, such that All Hunt Stag, rather than All Hunt Hare, becomes the state with the largest basin of attraction. Although this latter claim may seem unintuitive, it makes sense upon reflection. It's wrong to think that, with respect to sending signals, the only two possibilities are that the signals be meaningful (in the sense of a Lewis signaling system) or meaningless. If signals are correlated with hunting stag or hare, and strategies allow one to condition one's response upon the signal received, then the only time when receipt of a signal fails to convey information is in the special case where all combinations of signals and responses occur with equal frequency. In all other cases, signals – even if they are “meaningless” in the sense of a Lewis-style signaling system – become correlated with response-types, and convey information. The full effects of cheap talk, though, remain an open question.

PART III: ASSOCATION

Part III addresses the second conjunct of the title – the evolution of social structure. This work, carried out in collaboration with Robin Pemantle, considers how social structures, like those appealed to in the local interaction models of Part I, come about. The model is as follows: given a population, each person assigns a numeric weight to every other player in the population. These weights, if all non-negative (and with a sum strictly greater than zero), can be converted into interaction probabilities by straightforward normalization; if the weights are negative, interaction probabilities can be obtained with a minor amount of fiddling. People choose to play a game with others according to these interaction probabilities. After each interaction, some of the players (either just the initiator, or both, depending on the model) receives a payoff. These payoffs are used by the players to adjust the weights they assign to each other. As the weights increase, and weight tends to concentrate on some players rather than others, interaction structures emerge. The final chapter considers what happens when strategic dynamics (i.e. learning by Best Response, Imitate-the-best, or other learning rules) are combined with structural dynamics.

Much can be said about the technical content of the final two chapters, which cover a great deal of original and interesting material. Since, however, this would be of little benefit to readers unfamiliar with the book, I shall concentrate on a few overarching philosophical questions which, to my mind, remain unanswered.

First, regarding the caveat mentioned earlier: although we do get, in part I, a story about how social structure influences the evolution of justice and cooperation, and we do get, in part III, a story of how social structure might emerge, how well do the two stories line up? For starters, the interaction structures considered in part I are highly regular: two-dimensional square lattices (or toruses) or one-dimensional lines (or rings). The social structures which are shown to evolve in part III lack any such topological regularity. The emergence of justice and cooperation according to the local interaction models of part I is unlikely, then, if the model of social structure formation is that of part III. Moreover, the interaction model of part I is strictly deterministic, with the interactions being hard-wired and always taking place in each generation. How might a probabilistic model of the evolution of social structure like that of Part III be modified to give rise to deterministic interaction structures within a reasonable (i.e. human) time-frame, rather than in the infinite limit?Footnote ⁶

Second, a different concern regarding the type of explanation offered. The penultimate section of chapter 3 ends with the statement, “[t]he structure of local interaction makes a difference” (Reference SkyrmsSkyrms 2004: 42). This sentiment ramifies over the course of the book. We find that signals make a difference. The co-evolution of strategy and structure makes a difference. The relative rate of the co-evolution of strategy and structure makes a difference. How are we to assimilate all of these things-which-make-a-difference into a coherent explanatory account of cooperation, collective action, and the problem of the social contract? This remains unclear.

Consider, by way of comparison, the following crude way of putting the meta-narrative of Evolution of the Social Contract. The replicator dynamics are a model of cultural evolution. Strategies (i.e. behaviors) which have very large basins of attraction are highly likely to evolve, if the initial conditions were selected at random. Many behaviors of interest, such as fair division in resource allocation problems, retribution in the ultimatum game, and coordination upon meaningful signaling systems, turn out to evolve Lo and behold! often with surprising frequency – under the replicator dynamics. And, thus, we have an explanation for how certain core features of society could have come about through the operation of a blind, dumb, gradual process of social evolution.

It's not at all clear that The Stag Hunt permits anything like a similarly crude meta-narrative to be formulated. And perhaps this is a good thing. (Although I'm no postmodernist, I'm suspicious of grand meta-narratives, myself.) However, this also means that it's difficult to see exactly how the explanation works. If everything makes a difference, then all of the various parameters which factor into the evolution need to be set just so in order for us to find the behavior we find in society. Yet if only a very small set of possible paths leads from the primordial state to our current social state, what have we discovered? We already know that at least one such path exists, namely, whatever path we followed to get us here. If too many things make a difference, the project, then, risks becoming a game-theoretic archaeology for the human sciences (no – not in the sense of Foucault!) instead of a descriptive or predictive science facilitating substantive claims about future social states. At least that's a worry.

No work of philosophy shorter than the completed autobiography of Tristram Shandy can hope to answer all questions, and good work in philosophy raises more questions than it answers. As a snapshot of the recent state-of-the-art in evolutionary game theory, and the philosophical applications thereof, The Stag Hunt manages to surpass its predecessor in both scope and content. If only George Lucas had been so successful.